Approximation to the Mean and Variance of the Estimators Related to Gamma Distribution

 In this thesis, we study the gamma distribution because it has many applications in life – testing, survival and reliability investigation that appear in medical studies of chronic diseases and industrial life – testing. Approximation to the mean and variance of moments method estimators is made theoretically by using Taylor series expansion approximated up to second partial derivatives. The maximum likelihood estimators are derived and compared with several estimators that proposed in the literature. Where the practice show that the bias values of moment method estimators are adequate with the simulated bias values for moderate and large sample. While the variance values of the scale parameter are excellent in comparison with the simulated values.
A new bias corrected estimator based on the maximum likelihood estimator is suggested and show better performance in comparison with the other estimators proposed by McCullagh ,Nelder, Cardeiro, and Pearson.The theoretical results are tested by using Monte – Carlo simulation and compared by utilizing the measurement of mean square error.